Solve (-1/2+3/4)div-1-1/2*(-3/2+frac{1}{4})

$$( - \frac { 1 } { 2 } + \frac { 3 } { 4 } ) \div - 1 - \frac { 1 } { 2 } \times ( - \frac { 3 } { 2 } + \frac { 1 } { 4 } )$$

Evaluate

$$\frac{3}{8}=0.375$$

Solution Steps

Least common multiple of 2 and 4 is 4. Convert -\frac{1}{2} and \frac{3}{4} to fractions with denominator 4.

$$\frac{-\frac{2}{4}+\frac{3}{4}}{-1}-\frac{1}{2}\left(-\frac{3}{2}+\frac{1}{4}\right)$$

Since -\frac{2}{4} and \frac{3}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{-2+3}{4}}{-1}-\frac{1}{2}\left(-\frac{3}{2}+\frac{1}{4}\right)$$

Add -2 and 3 to get 1.

$$\frac{\frac{1}{4}}{-1}-\frac{1}{2}\left(-\frac{3}{2}+\frac{1}{4}\right)$$

Express \frac{\frac{1}{4}}{-1} as a single fraction.

$$\frac{1}{4\left(-1\right)}-\frac{1}{2}\left(-\frac{3}{2}+\frac{1}{4}\right)$$

Multiply 4 and -1 to get -4.

$$\frac{1}{-4}-\frac{1}{2}\left(-\frac{3}{2}+\frac{1}{4}\right)$$

Fraction \frac{1}{-4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

$$-\frac{1}{4}-\frac{1}{2}\left(-\frac{3}{2}+\frac{1}{4}\right)$$

Least common multiple of 2 and 4 is 4. Convert -\frac{3}{2} and \frac{1}{4} to fractions with denominator 4.

$$-\frac{1}{4}-\frac{1}{2}\left(-\frac{6}{4}+\frac{1}{4}\right)$$

Since -\frac{6}{4} and \frac{1}{4} have the same denominator, add them by adding their numerators.

$$-\frac{1}{4}-\frac{1}{2}\times \frac{-6+1}{4}$$

Add -6 and 1 to get -5.

$$-\frac{1}{4}-\frac{1}{2}\left(-\frac{5}{4}\right)$$

Multiply \frac{1}{2} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{1}{4}-\frac{1\left(-5\right)}{2\times 4}$$

Do the multiplications in the fraction \frac{1\left(-5\right)}{2\times 4}.

$$-\frac{1}{4}-\frac{-5}{8}$$

Fraction \frac{-5}{8} can be rewritten as -\frac{5}{8} by extracting the negative sign.

$$-\frac{1}{4}-\left(-\frac{5}{8}\right)$$

The opposite of -\frac{5}{8} is \frac{5}{8}.

$$-\frac{1}{4}+\frac{5}{8}$$

Least common multiple of 4 and 8 is 8. Convert -\frac{1}{4} and \frac{5}{8} to fractions with denominator 8.

$$-\frac{2}{8}+\frac{5}{8}$$

Since -\frac{2}{8} and \frac{5}{8} have the same denominator, add them by adding their numerators.

$$\frac{-2+5}{8}$$

Add -2 and 5 to get 3.

$$\frac{3}{8}$$

Factor

$$\frac{3}{2 ^ {3}} = 0.375$$